Solve sqrt[3]{2^28+2^30/10}é

$$\sqrt[ 3 ] { \frac { 2 ^ { 28 } + 2 ^ { 30 } } { 10 } } é$$

Evaluate

$$512é$$

Solution Steps

Calculate 2 to the power of 28 and get 268435456.

$$\sqrt[3]{\frac{268435456+2^{30}}{10}}é$$

Calculate 2 to the power of 30 and get 1073741824.

$$\sqrt[3]{\frac{268435456+1073741824}{10}}é$$

Add 268435456 and 1073741824 to get 1342177280.

$$\sqrt[3]{\frac{1342177280}{10}}é$$

Divide 1342177280 by 10 to get 134217728.

$$\sqrt[3]{134217728}é$$

Calculate \sqrt[3]{134217728} and get 512.

$$512é$$

Differentiate w.r.t. é

$$512$$

Steps Using Definition of a Derivative

Calculate 2 to the power of 28 and get 268435456.

$$\frac{\mathrm{d}}{\mathrm{d}é}(\sqrt[3]{\frac{268435456+2^{30}}{10}}é)$$

Calculate 2 to the power of 30 and get 1073741824.

$$\frac{\mathrm{d}}{\mathrm{d}é}(\sqrt[3]{\frac{268435456+1073741824}{10}}é)$$

Add 268435456 and 1073741824 to get 1342177280.

$$\frac{\mathrm{d}}{\mathrm{d}é}(\sqrt[3]{\frac{1342177280}{10}}é)$$

Divide 1342177280 by 10 to get 134217728.

$$\frac{\mathrm{d}}{\mathrm{d}é}(\sqrt[3]{134217728}é)$$

Calculate \sqrt[3]{134217728} and get 512.

$$\frac{\mathrm{d}}{\mathrm{d}é}(512é)$$

The derivative of ax^{n} is nax^{n-1}.

$$512é^{1-1}$$

Subtract 1 from 1.

$$512é^{0}$$

For any term t except 0, t^{0}=1.

$$512\times 1$$

For any term t, t\times 1=t and 1t=t.

$$512$$